Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1249,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.3 | ||
Root | \(-2.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1249 |
Dual form | 1950.2.e.p.1249.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 1.70156i | − 0.643130i | −0.946888 | − | 0.321565i | \(-0.895791\pi\) | ||||
0.946888 | − | 0.321565i | \(-0.104209\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70156 | −0.513040 | −0.256520 | − | 0.966539i | \(-0.582576\pi\) | ||||
−0.256520 | + | 0.966539i | \(0.582576\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 1.70156 | 0.454762 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.70156i | 1.38283i | 0.722457 | + | 0.691416i | \(0.243013\pi\) | ||||
−0.722457 | + | 0.691416i | \(0.756987\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −4.70156 | −1.07861 | −0.539306 | − | 0.842110i | \(-0.681313\pi\) | ||||
−0.539306 | + | 0.842110i | \(0.681313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70156 | −0.371311 | ||||||||
\(22\) | − 1.70156i | − 0.362774i | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.70156i | 0.321565i | ||||||||
\(29\) | −6.40312 | −1.18903 | −0.594515 | − | 0.804084i | \(-0.702656\pi\) | ||||
−0.594515 | + | 0.804084i | \(0.702656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.10469 | 1.63525 | 0.817625 | − | 0.575751i | \(-0.195290\pi\) | ||||
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.70156i | 0.296204i | ||||||||
\(34\) | −5.70156 | −0.977810 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.70156i | 0.772932i | 0.922304 | + | 0.386466i | \(0.126304\pi\) | ||||
−0.922304 | + | 0.386466i | \(0.873696\pi\) | |||||||
\(38\) | − 4.70156i | − 0.762694i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.70156 | 0.421913 | 0.210957 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210957 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(42\) | − 1.70156i | − 0.262557i | ||||||||
\(43\) | − 1.40312i | − 0.213974i | −0.994260 | − | 0.106987i | \(-0.965880\pi\) | ||||
0.994260 | − | 0.106987i | \(-0.0341204\pi\) | |||||||
\(44\) | 1.70156 | 0.256520 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 4.10469 | 0.586384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.70156 | 0.798378 | ||||||||
\(52\) | − 1.00000i | − 0.138675i | ||||||||
\(53\) | 10.4031i | 1.42898i | 0.699646 | + | 0.714490i | \(0.253341\pi\) | ||||
−0.699646 | + | 0.714490i | \(0.746659\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.70156 | −0.227381 | ||||||||
\(57\) | 4.70156i | 0.622737i | ||||||||
\(58\) | − 6.40312i | − 0.840771i | ||||||||
\(59\) | 3.70156 | 0.481902 | 0.240951 | − | 0.970537i | \(-0.422541\pi\) | ||||
0.240951 | + | 0.970537i | \(0.422541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.10469 | −0.653588 | −0.326794 | − | 0.945096i | \(-0.605968\pi\) | ||||
−0.326794 | + | 0.945096i | \(0.605968\pi\) | |||||||
\(62\) | 9.10469i | 1.15630i | ||||||||
\(63\) | 1.70156i | 0.214377i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.70156 | −0.209448 | ||||||||
\(67\) | 6.40312i | 0.782266i | 0.920334 | + | 0.391133i | \(0.127917\pi\) | ||||
−0.920334 | + | 0.391133i | \(0.872083\pi\) | |||||||
\(68\) | − 5.70156i | − 0.691416i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.70156 | 0.557973 | 0.278986 | − | 0.960295i | \(-0.410002\pi\) | ||||
0.278986 | + | 0.960295i | \(0.410002\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 12.0000i | 1.40449i | 0.711934 | + | 0.702247i | \(0.247820\pi\) | ||||
−0.711934 | + | 0.702247i | \(0.752180\pi\) | |||||||
\(74\) | −4.70156 | −0.546545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.70156 | 0.539306 | ||||||||
\(77\) | 2.89531i | 0.329952i | ||||||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | −0.701562 | −0.0789319 | −0.0394660 | − | 0.999221i | \(-0.512566\pi\) | ||||
−0.0394660 | + | 0.999221i | \(0.512566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.70156i | 0.298338i | ||||||||
\(83\) | 4.29844i | 0.471815i | 0.971776 | + | 0.235907i | \(0.0758062\pi\) | ||||
−0.971776 | + | 0.235907i | \(0.924194\pi\) | |||||||
\(84\) | 1.70156 | 0.185656 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.40312 | 0.151303 | ||||||||
\(87\) | 6.40312i | 0.686487i | ||||||||
\(88\) | 1.70156i | 0.181387i | ||||||||
\(89\) | 1.40312 | 0.148731 | 0.0743654 | − | 0.997231i | \(-0.476307\pi\) | ||||
0.0743654 | + | 0.997231i | \(0.476307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.70156 | 0.178372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 9.10469i | − 0.944112i | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 15.4031i | − 1.56395i | −0.623310 | − | 0.781975i | \(-0.714212\pi\) | ||||
0.623310 | − | 0.781975i | \(-0.285788\pi\) | |||||||
\(98\) | 4.10469i | 0.414636i | ||||||||
\(99\) | 1.70156 | 0.171013 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.298438 | 0.0296957 | 0.0148478 | − | 0.999890i | \(-0.495274\pi\) | ||||
0.0148478 | + | 0.999890i | \(0.495274\pi\) | |||||||
\(102\) | 5.70156i | 0.564539i | ||||||||
\(103\) | 11.4031i | 1.12358i | 0.827279 | + | 0.561792i | \(0.189888\pi\) | ||||
−0.827279 | + | 0.561792i | \(0.810112\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4031 | −1.01044 | ||||||||
\(107\) | − 0.104686i | − 0.0101204i | −0.999987 | − | 0.00506021i | \(-0.998389\pi\) | ||||
0.999987 | − | 0.00506021i | \(-0.00161072\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −10.7016 | −1.02502 | −0.512512 | − | 0.858680i | \(-0.671285\pi\) | ||||
−0.512512 | + | 0.858680i | \(0.671285\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.70156 | 0.446253 | ||||||||
\(112\) | − 1.70156i | − 0.160783i | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | −4.70156 | −0.440342 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.40312 | 0.594515 | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | 3.70156i | 0.340756i | ||||||||
\(119\) | 9.70156 | 0.889341 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.10469 | −0.736790 | ||||||||
\(122\) | − 5.10469i | − 0.462157i | ||||||||
\(123\) | − 2.70156i | − 0.243592i | ||||||||
\(124\) | −9.10469 | −0.817625 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.70156 | −0.151587 | ||||||||
\(127\) | − 12.7016i | − 1.12708i | −0.826088 | − | 0.563541i | \(-0.809439\pi\) | ||||
0.826088 | − | 0.563541i | \(-0.190561\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −1.40312 | −0.123538 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.50781 | −0.830701 | −0.415351 | − | 0.909661i | \(-0.636341\pi\) | ||||
−0.415351 | + | 0.909661i | \(0.636341\pi\) | |||||||
\(132\) | − 1.70156i | − 0.148102i | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −6.40312 | −0.553146 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.70156 | 0.488905 | ||||||||
\(137\) | 7.29844i | 0.623548i | 0.950156 | + | 0.311774i | \(0.100923\pi\) | ||||
−0.950156 | + | 0.311774i | \(0.899077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.40312 | 0.288649 | 0.144325 | − | 0.989530i | \(-0.453899\pi\) | ||||
0.144325 | + | 0.989530i | \(0.453899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 4.70156i | 0.394546i | ||||||||
\(143\) | − 1.70156i | − 0.142292i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | − 4.10469i | − 0.338549i | ||||||||
\(148\) | − 4.70156i | − 0.386466i | ||||||||
\(149\) | −19.4031 | −1.58957 | −0.794783 | − | 0.606894i | \(-0.792415\pi\) | ||||
−0.794783 | + | 0.606894i | \(0.792415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.10469 | 0.415413 | 0.207707 | − | 0.978191i | \(-0.433400\pi\) | ||||
0.207707 | + | 0.978191i | \(0.433400\pi\) | |||||||
\(152\) | 4.70156i | 0.381347i | ||||||||
\(153\) | − 5.70156i | − 0.460944i | ||||||||
\(154\) | −2.89531 | −0.233311 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | − 16.2984i | − 1.30076i | −0.759610 | − | 0.650378i | \(-0.774610\pi\) | ||||
0.759610 | − | 0.650378i | \(-0.225390\pi\) | |||||||
\(158\) | − 0.701562i | − 0.0558133i | ||||||||
\(159\) | 10.4031 | 0.825021 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 6.80625i | − 0.533107i | −0.963820 | − | 0.266553i | \(-0.914115\pi\) | ||||
0.963820 | − | 0.266553i | \(-0.0858848\pi\) | |||||||
\(164\) | −2.70156 | −0.210957 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.29844 | −0.333623 | ||||||||
\(167\) | 18.1047i | 1.40098i | 0.713661 | + | 0.700491i | \(0.247036\pi\) | ||||
−0.713661 | + | 0.700491i | \(0.752964\pi\) | |||||||
\(168\) | 1.70156i | 0.131278i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.70156 | 0.359537 | ||||||||
\(172\) | 1.40312i | 0.106987i | ||||||||
\(173\) | 25.8062i | 1.96201i | 0.193976 | + | 0.981006i | \(0.437862\pi\) | ||||
−0.193976 | + | 0.981006i | \(0.562138\pi\) | |||||||
\(174\) | −6.40312 | −0.485420 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.70156 | −0.128260 | ||||||||
\(177\) | − 3.70156i | − 0.278226i | ||||||||
\(178\) | 1.40312i | 0.105169i | ||||||||
\(179\) | −14.2094 | −1.06206 | −0.531029 | − | 0.847354i | \(-0.678195\pi\) | ||||
−0.531029 | + | 0.847354i | \(0.678195\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7016 | 1.31575 | 0.657873 | − | 0.753129i | \(-0.271456\pi\) | ||||
0.657873 | + | 0.753129i | \(0.271456\pi\) | |||||||
\(182\) | 1.70156i | 0.126128i | ||||||||
\(183\) | 5.10469i | 0.377349i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.10469 | 0.667588 | ||||||||
\(187\) | − 9.70156i | − 0.709448i | ||||||||
\(188\) | − 7.00000i | − 0.510527i | ||||||||
\(189\) | 1.70156 | 0.123770 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8062 | 0.926628 | 0.463314 | − | 0.886194i | \(-0.346660\pi\) | ||||
0.463314 | + | 0.886194i | \(0.346660\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 22.2094i | 1.59867i | 0.600889 | + | 0.799333i | \(0.294814\pi\) | ||||
−0.600889 | + | 0.799333i | \(0.705186\pi\) | |||||||
\(194\) | 15.4031 | 1.10588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.10469 | −0.293192 | ||||||||
\(197\) | 7.40312i | 0.527451i | 0.964598 | + | 0.263725i | \(0.0849513\pi\) | ||||
−0.964598 | + | 0.263725i | \(0.915049\pi\) | |||||||
\(198\) | 1.70156i | 0.120925i | ||||||||
\(199\) | −14.7016 | −1.04217 | −0.521083 | − | 0.853506i | \(-0.674472\pi\) | ||||
−0.521083 | + | 0.853506i | \(0.674472\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.40312 | 0.451642 | ||||||||
\(202\) | 0.298438i | 0.0209980i | ||||||||
\(203\) | 10.8953i | 0.764701i | ||||||||
\(204\) | −5.70156 | −0.399189 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.4031 | −0.794493 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8062 | −1.29468 | −0.647338 | − | 0.762203i | \(-0.724118\pi\) | ||||
−0.647338 | + | 0.762203i | \(0.724118\pi\) | |||||||
\(212\) | − 10.4031i | − 0.714490i | ||||||||
\(213\) | − 4.70156i | − 0.322146i | ||||||||
\(214\) | 0.104686 | 0.00715621 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − 15.4922i | − 1.05168i | ||||||||
\(218\) | − 10.7016i | − 0.724801i | ||||||||
\(219\) | 12.0000 | 0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.70156 | −0.383529 | ||||||||
\(222\) | 4.70156i | 0.315548i | ||||||||
\(223\) | 1.40312i | 0.0939601i | 0.998896 | + | 0.0469801i | \(0.0149597\pi\) | ||||
−0.998896 | + | 0.0469801i | \(0.985040\pi\) | |||||||
\(224\) | 1.70156 | 0.113690 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | 3.10469i | 0.206065i | 0.994678 | + | 0.103033i | \(0.0328546\pi\) | ||||
−0.994678 | + | 0.103033i | \(0.967145\pi\) | |||||||
\(228\) | − 4.70156i | − 0.311369i | ||||||||
\(229\) | −9.29844 | −0.614458 | −0.307229 | − | 0.951636i | \(-0.599402\pi\) | ||||
−0.307229 | + | 0.951636i | \(0.599402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.89531 | 0.190498 | ||||||||
\(232\) | 6.40312i | 0.420386i | ||||||||
\(233\) | − 18.2094i | − 1.19294i | −0.802637 | − | 0.596468i | \(-0.796570\pi\) | ||||
0.802637 | − | 0.596468i | \(-0.203430\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.70156 | −0.240951 | ||||||||
\(237\) | 0.701562i | 0.0455714i | ||||||||
\(238\) | 9.70156i | 0.628859i | ||||||||
\(239\) | 13.1047 | 0.847672 | 0.423836 | − | 0.905739i | \(-0.360683\pi\) | ||||
0.423836 | + | 0.905739i | \(0.360683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4031 | −0.992202 | −0.496101 | − | 0.868265i | \(-0.665236\pi\) | ||||
−0.496101 | + | 0.868265i | \(0.665236\pi\) | |||||||
\(242\) | − 8.10469i | − 0.520989i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 5.10469 | 0.326794 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.70156 | 0.172245 | ||||||||
\(247\) | − 4.70156i | − 0.299153i | ||||||||
\(248\) | − 9.10469i | − 0.578148i | ||||||||
\(249\) | 4.29844 | 0.272402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.70156 | 0.422999 | 0.211499 | − | 0.977378i | \(-0.432165\pi\) | ||||
0.211499 | + | 0.977378i | \(0.432165\pi\) | |||||||
\(252\) | − 1.70156i | − 0.107188i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.7016 | 0.796967 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 21.7016i | − 1.35371i | −0.736118 | − | 0.676853i | \(-0.763343\pi\) | ||||
0.736118 | − | 0.676853i | \(-0.236657\pi\) | |||||||
\(258\) | − 1.40312i | − 0.0873547i | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.40312 | 0.396343 | ||||||||
\(262\) | − 9.50781i | − 0.587395i | ||||||||
\(263\) | − 2.00000i | − 0.123325i | −0.998097 | − | 0.0616626i | \(-0.980360\pi\) | ||||
0.998097 | − | 0.0616626i | \(-0.0196403\pi\) | |||||||
\(264\) | 1.70156 | 0.104724 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.00000 | −0.490511 | ||||||||
\(267\) | − 1.40312i | − 0.0858698i | ||||||||
\(268\) | − 6.40312i | − 0.391133i | ||||||||
\(269\) | 7.20937 | 0.439563 | 0.219782 | − | 0.975549i | \(-0.429466\pi\) | ||||
0.219782 | + | 0.975549i | \(0.429466\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5078 | −0.759795 | −0.379898 | − | 0.925029i | \(-0.624041\pi\) | ||||
−0.379898 | + | 0.925029i | \(0.624041\pi\) | |||||||
\(272\) | 5.70156i | 0.345708i | ||||||||
\(273\) | − 1.70156i | − 0.102983i | ||||||||
\(274\) | −7.29844 | −0.440915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 22.0000i | − 1.32185i | −0.750451 | − | 0.660926i | \(-0.770164\pi\) | ||||
0.750451 | − | 0.660926i | \(-0.229836\pi\) | |||||||
\(278\) | 3.40312i | 0.204106i | ||||||||
\(279\) | −9.10469 | −0.545083 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9109 | 1.36675 | 0.683376 | − | 0.730067i | \(-0.260511\pi\) | ||||
0.683376 | + | 0.730067i | \(0.260511\pi\) | |||||||
\(282\) | 7.00000i | 0.416844i | ||||||||
\(283\) | − 8.59688i | − 0.511031i | −0.966805 | − | 0.255516i | \(-0.917755\pi\) | ||||
0.966805 | − | 0.255516i | \(-0.0822452\pi\) | |||||||
\(284\) | −4.70156 | −0.278986 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.70156 | 0.100615 | ||||||||
\(287\) | − 4.59688i | − 0.271345i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −15.5078 | −0.912224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.4031 | −0.902947 | ||||||||
\(292\) | − 12.0000i | − 0.702247i | ||||||||
\(293\) | − 8.59688i | − 0.502235i | −0.967957 | − | 0.251117i | \(-0.919202\pi\) | ||||
0.967957 | − | 0.251117i | \(-0.0807980\pi\) | |||||||
\(294\) | 4.10469 | 0.239390 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.70156 | 0.273273 | ||||||||
\(297\) | − 1.70156i | − 0.0987346i | ||||||||
\(298\) | − 19.4031i | − 1.12399i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.38750 | −0.137613 | ||||||||
\(302\) | 5.10469i | 0.293742i | ||||||||
\(303\) | − 0.298438i | − 0.0171448i | ||||||||
\(304\) | −4.70156 | −0.269653 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.70156 | 0.325937 | ||||||||
\(307\) | 0.701562i | 0.0400403i | 0.999800 | + | 0.0200201i | \(0.00637303\pi\) | ||||
−0.999800 | + | 0.0200201i | \(0.993627\pi\) | |||||||
\(308\) | − 2.89531i | − 0.164976i | ||||||||
\(309\) | 11.4031 | 0.648701 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | − 1.00000i | − 0.0566139i | ||||||||
\(313\) | − 17.2094i | − 0.972731i | −0.873755 | − | 0.486366i | \(-0.838322\pi\) | ||||
0.873755 | − | 0.486366i | \(-0.161678\pi\) | |||||||
\(314\) | 16.2984 | 0.919774 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.701562 | 0.0394660 | ||||||||
\(317\) | 26.8062i | 1.50559i | 0.658256 | + | 0.752794i | \(0.271295\pi\) | ||||
−0.658256 | + | 0.752794i | \(0.728705\pi\) | |||||||
\(318\) | 10.4031i | 0.583378i | ||||||||
\(319\) | 10.8953 | 0.610020 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.104686 | −0.00584302 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 26.8062i | − 1.49154i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.80625 | 0.376963 | ||||||||
\(327\) | 10.7016i | 0.591798i | ||||||||
\(328\) | − 2.70156i | − 0.149169i | ||||||||
\(329\) | 11.9109 | 0.656671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | − 4.29844i | − 0.235907i | ||||||||
\(333\) | − 4.70156i | − 0.257644i | ||||||||
\(334\) | −18.1047 | −0.990644 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.70156 | −0.0928278 | ||||||||
\(337\) | − 11.1047i | − 0.604911i | −0.953164 | − | 0.302455i | \(-0.902194\pi\) | ||||
0.953164 | − | 0.302455i | \(-0.0978063\pi\) | |||||||
\(338\) | − 1.00000i | − 0.0543928i | ||||||||
\(339\) | 14.0000 | 0.760376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.4922 | −0.838949 | ||||||||
\(342\) | 4.70156i | 0.254231i | ||||||||
\(343\) | − 18.8953i | − 1.02025i | ||||||||
\(344\) | −1.40312 | −0.0756514 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.8062 | −1.38735 | ||||||||
\(347\) | − 21.5078i | − 1.15460i | −0.816532 | − | 0.577300i | \(-0.804106\pi\) | ||||
0.816532 | − | 0.577300i | \(-0.195894\pi\) | |||||||
\(348\) | − 6.40312i | − 0.343243i | ||||||||
\(349\) | −1.40312 | −0.0751075 | −0.0375538 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375538 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | − 1.70156i | − 0.0906936i | ||||||||
\(353\) | 17.5078i | 0.931847i | 0.884825 | + | 0.465923i | \(0.154278\pi\) | ||||
−0.884825 | + | 0.465923i | \(0.845722\pi\) | |||||||
\(354\) | 3.70156 | 0.196736 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.40312 | −0.0743654 | ||||||||
\(357\) | − 9.70156i | − 0.513461i | ||||||||
\(358\) | − 14.2094i | − 0.750989i | ||||||||
\(359\) | −16.6125 | −0.876774 | −0.438387 | − | 0.898786i | \(-0.644450\pi\) | ||||
−0.438387 | + | 0.898786i | \(0.644450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.10469 | 0.163405 | ||||||||
\(362\) | 17.7016i | 0.930373i | ||||||||
\(363\) | 8.10469i | 0.425386i | ||||||||
\(364\) | −1.70156 | −0.0891861 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.10469 | −0.266826 | ||||||||
\(367\) | − 8.70156i | − 0.454218i | −0.973869 | − | 0.227109i | \(-0.927073\pi\) | ||||
0.973869 | − | 0.227109i | \(-0.0729273\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.70156 | −0.140638 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.7016 | 0.919019 | ||||||||
\(372\) | 9.10469i | 0.472056i | ||||||||
\(373\) | − 11.7016i | − 0.605884i | −0.953009 | − | 0.302942i | \(-0.902031\pi\) | ||||
0.953009 | − | 0.302942i | \(-0.0979688\pi\) | |||||||
\(374\) | 9.70156 | 0.501656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | − 6.40312i | − 0.329778i | ||||||||
\(378\) | 1.70156i | 0.0875189i | ||||||||
\(379\) | 33.1047 | 1.70047 | 0.850237 | − | 0.526400i | \(-0.176459\pi\) | ||||
0.850237 | + | 0.526400i | \(0.176459\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7016 | −0.650721 | ||||||||
\(382\) | 12.8062i | 0.655225i | ||||||||
\(383\) | − 0.492189i | − 0.0251497i | −0.999921 | − | 0.0125749i | \(-0.995997\pi\) | ||||
0.999921 | − | 0.0125749i | \(-0.00400281\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.2094 | −1.13043 | ||||||||
\(387\) | 1.40312i | 0.0713248i | ||||||||
\(388\) | 15.4031i | 0.781975i | ||||||||
\(389\) | 7.89531 | 0.400308 | 0.200154 | − | 0.979764i | \(-0.435856\pi\) | ||||
0.200154 | + | 0.979764i | \(0.435856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − 4.10469i | − 0.207318i | ||||||||
\(393\) | 9.50781i | 0.479606i | ||||||||
\(394\) | −7.40312 | −0.372964 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.70156 | −0.0855067 | ||||||||
\(397\) | 22.9109i | 1.14987i | 0.818200 | + | 0.574933i | \(0.194972\pi\) | ||||
−0.818200 | + | 0.574933i | \(0.805028\pi\) | |||||||
\(398\) | − 14.7016i | − 0.736923i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.2094 | −1.00921 | −0.504604 | − | 0.863351i | \(-0.668361\pi\) | ||||
−0.504604 | + | 0.863351i | \(0.668361\pi\) | |||||||
\(402\) | 6.40312i | 0.319359i | ||||||||
\(403\) | 9.10469i | 0.453537i | ||||||||
\(404\) | −0.298438 | −0.0148478 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8953 | −0.540725 | ||||||||
\(407\) | − 8.00000i | − 0.396545i | ||||||||
\(408\) | − 5.70156i | − 0.282269i | ||||||||
\(409\) | −16.5969 | −0.820663 | −0.410331 | − | 0.911937i | \(-0.634587\pi\) | ||||
−0.410331 | + | 0.911937i | \(0.634587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.29844 | 0.360005 | ||||||||
\(412\) | − 11.4031i | − 0.561792i | ||||||||
\(413\) | − 6.29844i | − 0.309926i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | − 3.40312i | − 0.166652i | ||||||||
\(418\) | 8.00000i | 0.391293i | ||||||||
\(419\) | 34.9109 | 1.70551 | 0.852755 | − | 0.522310i | \(-0.174930\pi\) | ||||
0.852755 | + | 0.522310i | \(0.174930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4031 | −0.653228 | −0.326614 | − | 0.945158i | \(-0.605908\pi\) | ||||
−0.326614 | + | 0.945158i | \(0.605908\pi\) | |||||||
\(422\) | − 18.8062i | − 0.915474i | ||||||||
\(423\) | − 7.00000i | − 0.340352i | ||||||||
\(424\) | 10.4031 | 0.505220 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.70156 | 0.227791 | ||||||||
\(427\) | 8.68594i | 0.420342i | ||||||||
\(428\) | 0.104686i | 0.00506021i | ||||||||
\(429\) | −1.70156 | −0.0821522 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3141 | −1.07483 | −0.537415 | − | 0.843318i | \(-0.680599\pi\) | ||||
−0.537415 | + | 0.843318i | \(0.680599\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − 8.10469i | − 0.389486i | −0.980854 | − | 0.194743i | \(-0.937613\pi\) | ||||
0.980854 | − | 0.194743i | \(-0.0623873\pi\) | |||||||
\(434\) | 15.4922 | 0.743649 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7016 | 0.512512 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.0000i | 0.573382i | ||||||||
\(439\) | 16.7016 | 0.797122 | 0.398561 | − | 0.917142i | \(-0.369510\pi\) | ||||
0.398561 | + | 0.917142i | \(0.369510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.10469 | −0.195461 | ||||||||
\(442\) | − 5.70156i | − 0.271196i | ||||||||
\(443\) | − 0.492189i | − 0.0233846i | −0.999932 | − | 0.0116923i | \(-0.996278\pi\) | ||||
0.999932 | − | 0.0116923i | \(-0.00372186\pi\) | |||||||
\(444\) | −4.70156 | −0.223126 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.40312 | −0.0664399 | ||||||||
\(447\) | 19.4031i | 0.917736i | ||||||||
\(448\) | 1.70156i | 0.0803913i | ||||||||
\(449\) | −8.70156 | −0.410652 | −0.205326 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205326 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.59688 | −0.216458 | ||||||||
\(452\) | − 14.0000i | − 0.658505i | ||||||||
\(453\) | − 5.10469i | − 0.239839i | ||||||||
\(454\) | −3.10469 | −0.145710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.70156 | 0.220171 | ||||||||
\(457\) | − 15.4031i | − 0.720528i | −0.932850 | − | 0.360264i | \(-0.882687\pi\) | ||||
0.932850 | − | 0.360264i | \(-0.117313\pi\) | |||||||
\(458\) | − 9.29844i | − 0.434487i | ||||||||
\(459\) | −5.70156 | −0.266126 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.20937 | −0.102901 | −0.0514504 | − | 0.998676i | \(-0.516384\pi\) | ||||
−0.0514504 | + | 0.998676i | \(0.516384\pi\) | |||||||
\(462\) | 2.89531i | 0.134702i | ||||||||
\(463\) | 27.7016i | 1.28740i | 0.765278 | + | 0.643700i | \(0.222602\pi\) | ||||
−0.765278 | + | 0.643700i | \(0.777398\pi\) | |||||||
\(464\) | −6.40312 | −0.297258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.2094 | 0.843533 | ||||||||
\(467\) | 36.7016i | 1.69835i | 0.528115 | + | 0.849173i | \(0.322899\pi\) | ||||
−0.528115 | + | 0.849173i | \(0.677101\pi\) | |||||||
\(468\) | 1.00000i | 0.0462250i | ||||||||
\(469\) | 10.8953 | 0.503099 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.2984 | −0.750992 | ||||||||
\(472\) | − 3.70156i | − 0.170378i | ||||||||
\(473\) | 2.38750i | 0.109778i | ||||||||
\(474\) | −0.701562 | −0.0322238 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.70156 | −0.444670 | ||||||||
\(477\) | − 10.4031i | − 0.476326i | ||||||||
\(478\) | 13.1047i | 0.599394i | ||||||||
\(479\) | −10.6125 | −0.484897 | −0.242449 | − | 0.970164i | \(-0.577951\pi\) | ||||
−0.242449 | + | 0.970164i | \(0.577951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.70156 | −0.214373 | ||||||||
\(482\) | − 15.4031i | − 0.701593i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.10469 | 0.368395 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − 27.1047i | − 1.22823i | −0.789216 | − | 0.614115i | \(-0.789513\pi\) | ||||
0.789216 | − | 0.614115i | \(-0.210487\pi\) | |||||||
\(488\) | 5.10469i | 0.231078i | ||||||||
\(489\) | −6.80625 | −0.307789 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5969 | 0.929524 | 0.464762 | − | 0.885436i | \(-0.346140\pi\) | ||||
0.464762 | + | 0.885436i | \(0.346140\pi\) | |||||||
\(492\) | 2.70156i | 0.121796i | ||||||||
\(493\) | − 36.5078i | − 1.64423i | ||||||||
\(494\) | 4.70156 | 0.211533 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.10469 | 0.408812 | ||||||||
\(497\) | − 8.00000i | − 0.358849i | ||||||||
\(498\) | 4.29844i | 0.192618i | ||||||||
\(499\) | 21.2094 | 0.949462 | 0.474731 | − | 0.880131i | \(-0.342545\pi\) | ||||
0.474731 | + | 0.880131i | \(0.342545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.1047 | 0.808858 | ||||||||
\(502\) | 6.70156i | 0.299105i | ||||||||
\(503\) | − 26.2094i | − 1.16862i | −0.811531 | − | 0.584309i | \(-0.801366\pi\) | ||||
0.811531 | − | 0.584309i | \(-0.198634\pi\) | |||||||
\(504\) | 1.70156 | 0.0757936 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | 12.7016i | 0.563541i | ||||||||
\(509\) | −7.40312 | −0.328138 | −0.164069 | − | 0.986449i | \(-0.552462\pi\) | ||||
−0.164069 | + | 0.986449i | \(0.552462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4187 | 0.903272 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 4.70156i | − 0.207579i | ||||||||
\(514\) | 21.7016 | 0.957215 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.40312 | 0.0617691 | ||||||||
\(517\) | − 11.9109i | − 0.523842i | ||||||||
\(518\) | 8.00000i | 0.351500i | ||||||||
\(519\) | 25.8062 | 1.13277 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.20937 | 0.0967944 | 0.0483972 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483972 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(522\) | 6.40312i | 0.280257i | ||||||||
\(523\) | − 0.806248i | − 0.0352548i | −0.999845 | − | 0.0176274i | \(-0.994389\pi\) | ||||
0.999845 | − | 0.0176274i | \(-0.00561126\pi\) | |||||||
\(524\) | 9.50781 | 0.415351 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | 51.9109i | 2.26128i | ||||||||
\(528\) | 1.70156i | 0.0740510i | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.70156 | −0.160634 | ||||||||
\(532\) | − 8.00000i | − 0.346844i | ||||||||
\(533\) | 2.70156i | 0.117018i | ||||||||
\(534\) | 1.40312 | 0.0607191 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.40312 | 0.276573 | ||||||||
\(537\) | 14.2094i | 0.613180i | ||||||||
\(538\) | 7.20937i | 0.310818i | ||||||||
\(539\) | −6.98438 | −0.300838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −40.2094 | −1.72874 | −0.864368 | − | 0.502860i | \(-0.832281\pi\) | ||||
−0.864368 | + | 0.502860i | \(0.832281\pi\) | |||||||
\(542\) | − 12.5078i | − 0.537256i | ||||||||
\(543\) | − 17.7016i | − 0.759647i | ||||||||
\(544\) | −5.70156 | −0.244452 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.70156 | 0.0728201 | ||||||||
\(547\) | 19.6125i | 0.838570i | 0.907855 | + | 0.419285i | \(0.137719\pi\) | ||||
−0.907855 | + | 0.419285i | \(0.862281\pi\) | |||||||
\(548\) | − 7.29844i | − 0.311774i | ||||||||
\(549\) | 5.10469 | 0.217863 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.1047 | 1.28250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.19375i | 0.0507635i | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.40312 | −0.144325 | ||||||||
\(557\) | − 8.80625i | − 0.373133i | −0.982442 | − | 0.186566i | \(-0.940264\pi\) | ||||
0.982442 | − | 0.186566i | \(-0.0597359\pi\) | |||||||
\(558\) | − 9.10469i | − 0.385432i | ||||||||
\(559\) | 1.40312 | 0.0593458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.70156 | −0.409600 | ||||||||
\(562\) | 22.9109i | 0.966439i | ||||||||
\(563\) | 0.492189i | 0.0207433i | 0.999946 | + | 0.0103717i | \(0.00330146\pi\) | ||||
−0.999946 | + | 0.0103717i | \(0.996699\pi\) | |||||||
\(564\) | −7.00000 | −0.294753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.59688 | 0.361354 | ||||||||
\(567\) | − 1.70156i | − 0.0714589i | ||||||||
\(568\) | − 4.70156i | − 0.197273i | ||||||||
\(569\) | 17.7016 | 0.742088 | 0.371044 | − | 0.928615i | \(-0.379000\pi\) | ||||
0.371044 | + | 0.928615i | \(0.379000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | 1.70156i | 0.0711459i | ||||||||
\(573\) | − 12.8062i | − 0.534989i | ||||||||
\(574\) | 4.59688 | 0.191870 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 14.2094i | − 0.591544i | −0.955259 | − | 0.295772i | \(-0.904423\pi\) | ||||
0.955259 | − | 0.295772i | \(-0.0955769\pi\) | |||||||
\(578\) | − 15.5078i | − 0.645040i | ||||||||
\(579\) | 22.2094 | 0.922990 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.31406 | 0.303438 | ||||||||
\(582\) | − 15.4031i | − 0.638480i | ||||||||
\(583\) | − 17.7016i | − 0.733124i | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.59688 | 0.355134 | ||||||||
\(587\) | 24.5078i | 1.01155i | 0.862667 | + | 0.505773i | \(0.168793\pi\) | ||||
−0.862667 | + | 0.505773i | \(0.831207\pi\) | |||||||
\(588\) | 4.10469i | 0.169274i | ||||||||
\(589\) | −42.8062 | −1.76380 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.40312 | 0.304524 | ||||||||
\(592\) | 4.70156i | 0.193233i | ||||||||
\(593\) | 26.9109i | 1.10510i | 0.833480 | + | 0.552550i | \(0.186345\pi\) | ||||
−0.833480 | + | 0.552550i | \(0.813655\pi\) | |||||||
\(594\) | 1.70156 | 0.0698159 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.4031 | 0.794783 | ||||||||
\(597\) | 14.7016i | 0.601695i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.2094 | 1.23432 | 0.617161 | − | 0.786837i | \(-0.288283\pi\) | ||||
0.617161 | + | 0.786837i | \(0.288283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.6125 | −1.65662 | −0.828309 | − | 0.560271i | \(-0.810697\pi\) | ||||
−0.828309 | + | 0.560271i | \(0.810697\pi\) | |||||||
\(602\) | − 2.38750i | − 0.0973074i | ||||||||
\(603\) | − 6.40312i | − 0.260755i | ||||||||
\(604\) | −5.10469 | −0.207707 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.298438 | 0.0121232 | ||||||||
\(607\) | − 15.8953i | − 0.645171i | −0.946540 | − | 0.322585i | \(-0.895448\pi\) | ||||
0.946540 | − | 0.322585i | \(-0.104552\pi\) | |||||||
\(608\) | − 4.70156i | − 0.190674i | ||||||||
\(609\) | 10.8953 | 0.441500 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | −0.283190 | ||||||||
\(612\) | 5.70156i | 0.230472i | ||||||||
\(613\) | − 12.8062i | − 0.517240i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) | ||||
0.965979 | − | 0.258620i | \(-0.0832677\pi\) | |||||||
\(614\) | −0.701562 | −0.0283127 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.89531 | 0.116656 | ||||||||
\(617\) | − 7.89531i | − 0.317853i | −0.987290 | − | 0.158927i | \(-0.949197\pi\) | ||||
0.987290 | − | 0.158927i | \(-0.0508033\pi\) | |||||||
\(618\) | 11.4031i | 0.458701i | ||||||||
\(619\) | 38.8062 | 1.55975 | 0.779877 | − | 0.625932i | \(-0.215281\pi\) | ||||
0.779877 | + | 0.625932i | \(0.215281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.0000i | 1.20289i | ||||||||
\(623\) | − 2.38750i | − 0.0956533i | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2094 | 0.687825 | ||||||||
\(627\) | − 8.00000i | − 0.319489i | ||||||||
\(628\) | 16.2984i | 0.650378i | ||||||||
\(629\) | −26.8062 | −1.06884 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6125 | −0.701142 | −0.350571 | − | 0.936536i | \(-0.614013\pi\) | ||||
−0.350571 | + | 0.936536i | \(0.614013\pi\) | |||||||
\(632\) | 0.701562i | 0.0279066i | ||||||||
\(633\) | 18.8062i | 0.747481i | ||||||||
\(634\) | −26.8062 | −1.06461 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10.4031 | −0.412511 | ||||||||
\(637\) | 4.10469i | 0.162634i | ||||||||
\(638\) | 10.8953i | 0.431350i | ||||||||
\(639\) | −4.70156 | −0.185991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5078 | −1.04700 | −0.523498 | − | 0.852027i | \(-0.675373\pi\) | ||||
−0.523498 | + | 0.852027i | \(0.675373\pi\) | |||||||
\(642\) | − 0.104686i | − 0.00413164i | ||||||||
\(643\) | 16.7016i | 0.658645i | 0.944217 | + | 0.329323i | \(0.106820\pi\) | ||||
−0.944217 | + | 0.329323i | \(0.893180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.8062 | 1.05468 | ||||||||
\(647\) | − 24.0000i | − 0.943537i | −0.881722 | − | 0.471769i | \(-0.843616\pi\) | ||||
0.881722 | − | 0.471769i | \(-0.156384\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −6.29844 | −0.247235 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4922 | −0.607187 | ||||||||
\(652\) | 6.80625i | 0.266553i | ||||||||
\(653\) | 27.7016i | 1.08405i | 0.840364 | + | 0.542023i | \(0.182341\pi\) | ||||
−0.840364 | + | 0.542023i | \(0.817659\pi\) | |||||||
\(654\) | −10.7016 | −0.418464 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.70156 | 0.105478 | ||||||||
\(657\) | − 12.0000i | − 0.468165i | ||||||||
\(658\) | 11.9109i | 0.464337i | ||||||||
\(659\) | −38.3141 | −1.49250 | −0.746252 | − | 0.665664i | \(-0.768149\pi\) | ||||
−0.746252 | + | 0.665664i | \(0.768149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.1203 | 1.67719 | 0.838593 | − | 0.544759i | \(-0.183379\pi\) | ||||
0.838593 | + | 0.544759i | \(0.183379\pi\) | |||||||
\(662\) | − 12.0000i | − 0.466393i | ||||||||
\(663\) | 5.70156i | 0.221430i | ||||||||
\(664\) | 4.29844 | 0.166812 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.70156 | 0.182182 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − 18.1047i | − 0.700491i | ||||||||
\(669\) | 1.40312 | 0.0542479 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.68594 | 0.335317 | ||||||||
\(672\) | − 1.70156i | − 0.0656392i | ||||||||
\(673\) | 28.0156i | 1.07992i | 0.841690 | + | 0.539961i | \(0.181561\pi\) | ||||
−0.841690 | + | 0.539961i | \(0.818439\pi\) | |||||||
\(674\) | 11.1047 | 0.427737 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | − 19.6125i | − 0.753769i | −0.926260 | − | 0.376885i | \(-0.876995\pi\) | ||||
0.926260 | − | 0.376885i | \(-0.123005\pi\) | |||||||
\(678\) | 14.0000i | 0.537667i | ||||||||
\(679\) | −26.2094 | −1.00582 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.10469 | 0.118972 | ||||||||
\(682\) | − 15.4922i | − 0.593227i | ||||||||
\(683\) | − 38.2984i | − 1.46545i | −0.680525 | − | 0.732724i | \(-0.738248\pi\) | ||||
0.680525 | − | 0.732724i | \(-0.261752\pi\) | |||||||
\(684\) | −4.70156 | −0.179769 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.8953 | 0.721426 | ||||||||
\(687\) | 9.29844i | 0.354758i | ||||||||
\(688\) | − 1.40312i | − 0.0534936i | ||||||||
\(689\) | −10.4031 | −0.396327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8062 | −1.81864 | −0.909318 | − | 0.416103i | \(-0.863396\pi\) | ||||
−0.909318 | + | 0.416103i | \(0.863396\pi\) | |||||||
\(692\) | − 25.8062i | − 0.981006i | ||||||||
\(693\) | − 2.89531i | − 0.109984i | ||||||||
\(694\) | 21.5078 | 0.816425 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.40312 | 0.242710 | ||||||||
\(697\) | 15.4031i | 0.583435i | ||||||||
\(698\) | − 1.40312i | − 0.0531090i | ||||||||
\(699\) | −18.2094 | −0.688742 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9109 | −0.525409 | −0.262704 | − | 0.964876i | \(-0.584614\pi\) | ||||
−0.262704 | + | 0.964876i | \(0.584614\pi\) | |||||||
\(702\) | − 1.00000i | − 0.0377426i | ||||||||
\(703\) | − 22.1047i | − 0.833694i | ||||||||
\(704\) | 1.70156 | 0.0641300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.5078 | −0.658915 | ||||||||
\(707\) | − 0.507811i | − 0.0190982i | ||||||||
\(708\) | 3.70156i | 0.139113i | ||||||||
\(709\) | 35.6125 | 1.33746 | 0.668728 | − | 0.743507i | \(-0.266839\pi\) | ||||
0.668728 | + | 0.743507i | \(0.266839\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.701562 | 0.0263106 | ||||||||
\(712\) | − 1.40312i | − 0.0525843i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 9.70156 | 0.363072 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.2094 | 0.531029 | ||||||||
\(717\) | − 13.1047i | − 0.489403i | ||||||||
\(718\) | − 16.6125i | − 0.619973i | ||||||||
\(719\) | −53.0156 | −1.97715 | −0.988575 | − | 0.150733i | \(-0.951837\pi\) | ||||
−0.988575 | + | 0.150733i | \(0.951837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.4031 | 0.722610 | ||||||||
\(722\) | 3.10469i | 0.115544i | ||||||||
\(723\) | 15.4031i | 0.572848i | ||||||||
\(724\) | −17.7016 | −0.657873 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.10469 | −0.300793 | ||||||||
\(727\) | 46.2094i | 1.71381i | 0.515474 | + | 0.856905i | \(0.327616\pi\) | ||||
−0.515474 | + | 0.856905i | \(0.672384\pi\) | |||||||
\(728\) | − 1.70156i | − 0.0630641i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | − 5.10469i | − 0.188675i | ||||||||
\(733\) | − 3.08907i | − 0.114097i | −0.998371 | − | 0.0570486i | \(-0.981831\pi\) | ||||
0.998371 | − | 0.0570486i | \(-0.0181690\pi\) | |||||||
\(734\) | 8.70156 | 0.321181 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 10.8953i | − 0.401334i | ||||||||
\(738\) | − 2.70156i | − 0.0994459i | ||||||||
\(739\) | 46.6125 | 1.71467 | 0.857334 | − | 0.514760i | \(-0.172119\pi\) | ||||
0.857334 | + | 0.514760i | \(0.172119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.70156 | −0.172716 | ||||||||
\(742\) | 17.7016i | 0.649845i | ||||||||
\(743\) | − 20.6125i | − 0.756199i | −0.925765 | − | 0.378100i | \(-0.876578\pi\) | ||||
0.925765 | − | 0.378100i | \(-0.123422\pi\) | |||||||
\(744\) | −9.10469 | −0.333794 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.7016 | 0.428425 | ||||||||
\(747\) | − 4.29844i | − 0.157272i | ||||||||
\(748\) | 9.70156i | 0.354724i | ||||||||
\(749\) | −0.178130 | −0.00650874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5078 | −0.857812 | −0.428906 | − | 0.903349i | \(-0.641101\pi\) | ||||
−0.428906 | + | 0.903349i | \(0.641101\pi\) | |||||||
\(752\) | 7.00000i | 0.255264i | ||||||||
\(753\) | − 6.70156i | − 0.244218i | ||||||||
\(754\) | 6.40312 | 0.233188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.70156 | −0.0618852 | ||||||||
\(757\) | − 37.1047i | − 1.34859i | −0.738461 | − | 0.674296i | \(-0.764447\pi\) | ||||
0.738461 | − | 0.674296i | \(-0.235553\pi\) | |||||||
\(758\) | 33.1047i | 1.20242i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.7172 | 1.58475 | 0.792373 | − | 0.610036i | \(-0.208845\pi\) | ||||
0.792373 | + | 0.610036i | \(0.208845\pi\) | |||||||
\(762\) | − 12.7016i | − 0.460129i | ||||||||
\(763\) | 18.2094i | 0.659224i | ||||||||
\(764\) | −12.8062 | −0.463314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.492189 | 0.0177835 | ||||||||
\(767\) | 3.70156i | 0.133656i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7016 | −0.781563 | ||||||||
\(772\) | − 22.2094i | − 0.799333i | ||||||||
\(773\) | − 39.4031i | − 1.41723i | −0.705594 | − | 0.708616i | \(-0.749320\pi\) | ||||
0.705594 | − | 0.708616i | \(-0.250680\pi\) | |||||||
\(774\) | −1.40312 | −0.0504343 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.4031 | −0.552940 | ||||||||
\(777\) | − 8.00000i | − 0.286998i | ||||||||
\(778\) | 7.89531i | 0.283061i | ||||||||
\(779\) | −12.7016 | −0.455081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 6.40312i | − 0.228829i | ||||||||
\(784\) | 4.10469 | 0.146596 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.50781 | −0.339132 | ||||||||
\(787\) | 53.1047i | 1.89298i | 0.322737 | + | 0.946489i | \(0.395397\pi\) | ||||
−0.322737 | + | 0.946489i | \(0.604603\pi\) | |||||||
\(788\) | − 7.40312i | − 0.263725i | ||||||||
\(789\) | −2.00000 | −0.0712019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.8219 | 0.847008 | ||||||||
\(792\) | − 1.70156i | − 0.0604624i | ||||||||
\(793\) | − 5.10469i | − 0.181273i | ||||||||
\(794\) | −22.9109 | −0.813079 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.7016 | 0.521083 | ||||||||
\(797\) | − 41.9109i | − 1.48456i | −0.670089 | − | 0.742281i | \(-0.733744\pi\) | ||||
0.670089 | − | 0.742281i | \(-0.266256\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | −39.9109 | −1.41195 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.40312 | −0.0495770 | ||||||||
\(802\) | − 20.2094i | − 0.713618i | ||||||||
\(803\) | − 20.4187i | − 0.720562i | ||||||||
\(804\) | −6.40312 | −0.225821 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.10469 | −0.320699 | ||||||||
\(807\) | − 7.20937i | − 0.253782i | ||||||||
\(808\) | − 0.298438i | − 0.0104990i | ||||||||
\(809\) | −32.8062 | −1.15341 | −0.576703 | − | 0.816954i | \(-0.695661\pi\) | ||||
−0.576703 | + | 0.816954i | \(0.695661\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.2984 | 1.48530 | 0.742650 | − | 0.669680i | \(-0.233569\pi\) | ||||
0.742650 | + | 0.669680i | \(0.233569\pi\) | |||||||
\(812\) | − 10.8953i | − 0.382351i | ||||||||
\(813\) | 12.5078i | 0.438668i | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.70156 | 0.199595 | ||||||||
\(817\) | 6.59688i | 0.230795i | ||||||||
\(818\) | − 16.5969i | − 0.580296i | ||||||||
\(819\) | −1.70156 | −0.0594574 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.4031 | −1.16578 | −0.582889 | − | 0.812552i | \(-0.698078\pi\) | ||||
−0.582889 | + | 0.812552i | \(0.698078\pi\) | |||||||
\(822\) | 7.29844i | 0.254562i | ||||||||
\(823\) | 2.10469i | 0.0733648i | 0.999327 | + | 0.0366824i | \(0.0116790\pi\) | ||||
−0.999327 | + | 0.0366824i | \(0.988321\pi\) | |||||||
\(824\) | 11.4031 | 0.397247 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.29844 | 0.219151 | ||||||||
\(827\) | 14.2984i | 0.497205i | 0.968606 | + | 0.248603i | \(0.0799713\pi\) | ||||
−0.968606 | + | 0.248603i | \(0.920029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.5078 | −0.920654 | −0.460327 | − | 0.887749i | \(-0.652268\pi\) | ||||
−0.460327 | + | 0.887749i | \(0.652268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.0000 | −0.763172 | ||||||||
\(832\) | − 1.00000i | − 0.0346688i | ||||||||
\(833\) | 23.4031i | 0.810870i | ||||||||
\(834\) | 3.40312 | 0.117841 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.00000 | −0.276686 | ||||||||
\(837\) | 9.10469i | 0.314704i | ||||||||
\(838\) | 34.9109i | 1.20598i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0000 | 0.413793 | ||||||||
\(842\) | − 13.4031i | − 0.461902i | ||||||||
\(843\) | − 22.9109i | − 0.789095i | ||||||||
\(844\) | 18.8062 | 0.647338 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | 13.7906i | 0.473852i | ||||||||
\(848\) | 10.4031i | 0.357245i | ||||||||
\(849\) | −8.59688 | −0.295044 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.70156i | 0.161073i | ||||||||
\(853\) | 31.5078i | 1.07881i | 0.842047 | + | 0.539403i | \(0.181350\pi\) | ||||
−0.842047 | + | 0.539403i | \(0.818650\pi\) | |||||||
\(854\) | −8.68594 | −0.297227 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.104686 | −0.00357811 | ||||||||
\(857\) | 43.6125i | 1.48977i | 0.667190 | + | 0.744887i | \(0.267497\pi\) | ||||
−0.667190 | + | 0.744887i | \(0.732503\pi\) | |||||||
\(858\) | − 1.70156i | − 0.0580904i | ||||||||
\(859\) | −32.2094 | −1.09897 | −0.549485 | − | 0.835504i | \(-0.685176\pi\) | ||||
−0.549485 | + | 0.835504i | \(0.685176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.59688 | −0.156661 | ||||||||
\(862\) | − 22.3141i | − 0.760020i | ||||||||
\(863\) | 48.2250i | 1.64160i | 0.571217 | + | 0.820799i | \(0.306471\pi\) | ||||
−0.571217 | + | 0.820799i | \(0.693529\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.10469 | 0.275408 | ||||||||
\(867\) | 15.5078i | 0.526673i | ||||||||
\(868\) | 15.4922i | 0.525839i | ||||||||
\(869\) | 1.19375 | 0.0404952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.40312 | −0.216962 | ||||||||
\(872\) | 10.7016i | 0.362401i | ||||||||
\(873\) | 15.4031i | 0.521317i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | 27.7172i | 0.935943i | 0.883744 | + | 0.467971i | \(0.155015\pi\) | ||||
−0.883744 | + | 0.467971i | \(0.844985\pi\) | |||||||
\(878\) | 16.7016i | 0.563650i | ||||||||
\(879\) | −8.59688 | −0.289965 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.7172 | 1.03489 | 0.517444 | − | 0.855717i | \(-0.326884\pi\) | ||||
0.517444 | + | 0.855717i | \(0.326884\pi\) | |||||||
\(882\) | − 4.10469i | − 0.138212i | ||||||||
\(883\) | 5.61250i | 0.188876i | 0.995531 | + | 0.0944378i | \(0.0301053\pi\) | ||||
−0.995531 | + | 0.0944378i | \(0.969895\pi\) | |||||||
\(884\) | 5.70156 | 0.191764 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.492189 | 0.0165354 | ||||||||
\(887\) | − 20.0000i | − 0.671534i | −0.941945 | − | 0.335767i | \(-0.891004\pi\) | ||||
0.941945 | − | 0.335767i | \(-0.108996\pi\) | |||||||
\(888\) | − 4.70156i | − 0.157774i | ||||||||
\(889\) | −21.6125 | −0.724860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.70156 | −0.0570045 | ||||||||
\(892\) | − 1.40312i | − 0.0469801i | ||||||||
\(893\) | − 32.9109i | − 1.10132i | ||||||||
\(894\) | −19.4031 | −0.648938 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.70156 | −0.0568452 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 8.70156i | − 0.290375i | ||||||||
\(899\) | −58.2984 | −1.94436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.3141 | −1.97604 | ||||||||
\(902\) | − 4.59688i | − 0.153059i | ||||||||
\(903\) | 2.38750i | 0.0794511i | ||||||||
\(904\) | 14.0000 | 0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.10469 | 0.169592 | ||||||||
\(907\) | 39.0156i | 1.29549i | 0.761856 | + | 0.647746i | \(0.224288\pi\) | ||||
−0.761856 | + | 0.647746i | \(0.775712\pi\) | |||||||
\(908\) | − 3.10469i | − 0.103033i | ||||||||
\(909\) | −0.298438 | −0.00989856 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.79063 | 0.125589 | 0.0627945 | − | 0.998026i | \(-0.479999\pi\) | ||||
0.0627945 | + | 0.998026i | \(0.479999\pi\) | |||||||
\(912\) | 4.70156i | 0.155684i | ||||||||
\(913\) | − 7.31406i | − 0.242060i | ||||||||
\(914\) | 15.4031 | 0.509490 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.29844 | 0.307229 | ||||||||
\(917\) | 16.1781i | 0.534249i | ||||||||
\(918\) | − 5.70156i | − 0.188180i | ||||||||
\(919\) | 24.1047 | 0.795140 | 0.397570 | − | 0.917572i | \(-0.369854\pi\) | ||||
0.397570 | + | 0.917572i | \(0.369854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.701562 | 0.0231173 | ||||||||
\(922\) | − 2.20937i | − 0.0727618i | ||||||||
\(923\) | 4.70156i | 0.154754i | ||||||||
\(924\) | −2.89531 | −0.0952488 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.7016 | −0.910330 | ||||||||
\(927\) | − 11.4031i | − 0.374528i | ||||||||
\(928\) | − 6.40312i | − 0.210193i | ||||||||
\(929\) | −58.7016 | −1.92594 | −0.962968 | − | 0.269616i | \(-0.913103\pi\) | ||||
−0.962968 | + | 0.269616i | \(0.913103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.2984 | −0.632481 | ||||||||
\(932\) | 18.2094i | 0.596468i | ||||||||
\(933\) | − 30.0000i | − 0.982156i | ||||||||
\(934\) | −36.7016 | −1.20091 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | − 29.9109i | − 0.977148i | −0.872523 | − | 0.488574i | \(-0.837517\pi\) | ||||
0.872523 | − | 0.488574i | \(-0.162483\pi\) | |||||||
\(938\) | 10.8953i | 0.355745i | ||||||||
\(939\) | −17.2094 | −0.561607 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.4187 | −1.57841 | −0.789203 | − | 0.614132i | \(-0.789506\pi\) | ||||
−0.789203 | + | 0.614132i | \(0.789506\pi\) | |||||||
\(942\) | − 16.2984i | − 0.531032i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.70156 | 0.120476 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.38750 | −0.0776244 | ||||||||
\(947\) | 15.4922i | 0.503429i | 0.967802 | + | 0.251714i | \(0.0809943\pi\) | ||||
−0.967802 | + | 0.251714i | \(0.919006\pi\) | |||||||
\(948\) | − 0.701562i | − 0.0227857i | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8062 | 0.869252 | ||||||||
\(952\) | − 9.70156i | − 0.314429i | ||||||||
\(953\) | 37.7016i | 1.22127i | 0.791911 | + | 0.610637i | \(0.209086\pi\) | ||||
−0.791911 | + | 0.610637i | \(0.790914\pi\) | |||||||
\(954\) | 10.4031 | 0.336814 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.1047 | −0.423836 | ||||||||
\(957\) | − 10.8953i | − 0.352195i | ||||||||
\(958\) | − 10.6125i | − 0.342874i | ||||||||
\(959\) | 12.4187 | 0.401022 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.8953 | 1.67404 | ||||||||
\(962\) | − 4.70156i | − 0.151584i | ||||||||
\(963\) | 0.104686i | 0.00337347i | ||||||||
\(964\) | 15.4031 | 0.496101 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.1047i | 1.57910i | 0.613686 | + | 0.789550i | \(0.289686\pi\) | ||||
−0.613686 | + | 0.789550i | \(0.710314\pi\) | |||||||
\(968\) | 8.10469i | 0.260494i | ||||||||
\(969\) | −26.8062 | −0.861141 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.1047 | −1.80049 | −0.900243 | − | 0.435389i | \(-0.856611\pi\) | ||||
−0.900243 | + | 0.435389i | \(0.856611\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 5.79063i | − 0.185639i | ||||||||
\(974\) | 27.1047 | 0.868490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.10469 | −0.163397 | ||||||||
\(977\) | − 10.5969i | − 0.339024i | −0.985528 | − | 0.169512i | \(-0.945781\pi\) | ||||
0.985528 | − | 0.169512i | \(-0.0542192\pi\) | |||||||
\(978\) | − 6.80625i | − 0.217640i | ||||||||
\(979\) | −2.38750 | −0.0763049 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7016 | 0.341675 | ||||||||
\(982\) | 20.5969i | 0.657273i | ||||||||
\(983\) | − 24.5078i | − 0.781678i | −0.920459 | − | 0.390839i | \(-0.872185\pi\) | ||||
0.920459 | − | 0.390839i | \(-0.127815\pi\) | |||||||
\(984\) | −2.70156 | −0.0861227 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.5078 | 1.16265 | ||||||||
\(987\) | − 11.9109i | − 0.379129i | ||||||||
\(988\) | 4.70156i | 0.149577i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.1047 | 0.320986 | 0.160493 | − | 0.987037i | \(-0.448692\pi\) | ||||
0.160493 | + | 0.987037i | \(0.448692\pi\) | |||||||
\(992\) | 9.10469i | 0.289074i | ||||||||
\(993\) | 12.0000i | 0.380808i | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.29844 | −0.136201 | ||||||||
\(997\) | − 42.5078i | − 1.34624i | −0.739535 | − | 0.673118i | \(-0.764955\pi\) | ||||
0.739535 | − | 0.673118i | \(-0.235045\pi\) | |||||||
\(998\) | 21.2094i | 0.671371i | ||||||||
\(999\) | −4.70156 | −0.148751 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.e.p.1249.3 | 4 | ||
3.2 | odd | 2 | 5850.2.e.bi.5149.1 | 4 | |||
5.2 | odd | 4 | 1950.2.a.bc.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1950.2.a.bg.1.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1950.2.e.p.1249.2 | 4 | ||
15.2 | even | 4 | 5850.2.a.cj.1.2 | 2 | |||
15.8 | even | 4 | 5850.2.a.cg.1.1 | 2 | |||
15.14 | odd | 2 | 5850.2.e.bi.5149.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.a.bc.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
1950.2.a.bg.1.1 | yes | 2 | 5.3 | odd | 4 | ||
1950.2.e.p.1249.2 | 4 | 5.4 | even | 2 | inner | ||
1950.2.e.p.1249.3 | 4 | 1.1 | even | 1 | trivial | ||
5850.2.a.cg.1.1 | 2 | 15.8 | even | 4 | |||
5850.2.a.cj.1.2 | 2 | 15.2 | even | 4 | |||
5850.2.e.bi.5149.1 | 4 | 3.2 | odd | 2 | |||
5850.2.e.bi.5149.4 | 4 | 15.14 | odd | 2 |